In summary, these data show that ATP players with both optimized racquet MgR/I value and high swingweight have significantly superior rankings compared to other players.

The raw data comes from a combined list of 99 Top-200 ATP pros whose racquet specs were posted either on Greg Raven's website, or by Jura in his 2005 Pro Racquet Specs post.
Swingweights for the players on Jura's list were approximated from M, R, and L using Rod Cross's 2-segment beam method.

Fig. 1 compares Performance vs MgR/I value for the 36 players on the list with swingweights in the 350-370 range. Of those 36 players, 25 had MgR/I less than 20.7, 10 were in the 20.7-21.1 range, and 1 was over 21.1. Statistically, the players in the 20.7-21.1 group have significantly superior rankings to those with lower MgR/I values.

Fig. 2 shows that ATP player racquet specs are clustered around the apparent optimal MgR/I range of about 20.9, while WTA player distribution is shifted toward a higher apparent optimum of about 21.1.

Fig. 3 shows that for the 53 ATP players on the list within the 'optimum' 20.7-21.1 MgR/I range, players with higher swingweights have superior rankings -- a very statistically significant result!

Fig. 4 shows that both ATP player and WTA player rankings correlate positively with increasing Effective Mass. For both men and women, Effective Mass of >160g (calculated 12cm from tip) seems to be key to performance. Note that Effective Mass is different than Swingweight, because an extended length racquet might have a high swingweight, but still have little mass in the racquethead. It also shows that players near the optimum MgR/I range benefit most from high effective mass.

Enjoy!

For instructions for tuning your frame to find your personal optimum value for MgR/I, see second post of this thread.

The MgR/I value gives a measure of the racquet's natural swing frequency as it pivots about the wrist axis on a forehand.

A groundstroke can be simply modeled as a double pendulum, with the upper pendulum swinging from the shoulder, and the lower pendulum swinging from the wrist. The speed of the upper pendulum is mostly related to the length of the player's arm, while the speed of the lower pendulum is largely a function of the racquet's weight's distribution. The angular acceleration of a pendulum is proportional to MgR/I, where M is the mass of the pendulum (here in kg), g is the acceleration of gravity (here assumed 980.5 cm/s^2), R is the distance from the pivot point to the center of mass (here in cm), and I is the moment of inertia about the pivot point (here equal to Swingweight + 20MR - 100M). Thus, a racquet's MgR/I value gives a measure of its natural swing frequency.

If MgR/I is perfectly tuned to the optimum value, the racquetface angle will naturally stay constant through the hitting zone, greatly improving accuracy. If MgR/I is too low, the racquethead will lag behind the hand unless the player compensates by applying a force from the wrist, making control more difficult and the forehand stroke more sensitive to timing errors. And if the MgR/I value is too high, the racquethead will naturally move through the hitting zone faster than the hand, also making the stroke difficult to control.

The optimum MgR/I value is not the same for every player. It depends on the player's height because players with longer arms have naturally slower swings. For players about 6'2" in height, I believe that the optimum MgR/I value is about 20.8 (this is supported by the data above). For players about 5'11" tall, I believe the optimum MgR/I value is about 21.0 (this is further supported by my own personal experimentation, as I stand 5'11" tall). And for players about 5'8" tall, I believe the optimum MgR/I value is about 21.2 (this is supported by my analysis of WTA specs, which I plan to post soon).

The optimum MgR/I value is also likely dependent on the player's style of stroke or grip . For example, for players with full western grips, the importance of optimizing MgR/I may be lessened, or the stroke may be optimized with a lower MgR/I value than for an eastern grip. But for players with eastern or weak semi-western grips, I believe optimizing MgR/I is more crucial. Also, choking up the the handle will increase the effective MgR/I value.

It's my belief that the optimal MR^2 zone of ~385 arises due to circumstance, because those pros that have both high swingweight (>350) and optimized MgR/I value (~21.0) tend to have racquets with MR^2 of about 385.

There are many pros with high swingweight but suboptimal MgR/I value. And there are many pros with optimized MgR/I value but low (suboptimal) swingweight. In both cases, the MR^2 value tends be less than 380.

My opinion is that it is well worth it to tune your MgR/I value to your personal optimum for your body and your swing.
Steps for Tuning MgR/I to find your personal optimum for your swing, for maximum control.

Step 1: Get accurate measurements of racquet mass M (kg), balance R (cm), and swingweight about axis through butt end of racquet (I).

Step 2 is to calculate how much weight should be placed on the handle to move the MgR/I value to ~21.0 (to get it close).

Step 3 is to make the modification.

Step 4 is to remeasure the specs and verify that you are close to 21.0.

Caution: You're not done yet, as the most important step still remains!

Step 5: Tuning the racquet on the court:

I recommend that you grab some extra lead tape and find a wall or racquetball court. You cannot tune the MgR/I value by hitting balls that you drop -- you need the balls to be coming at you with decent velocity in order to tune the angular velocity of your stroke, so a wall is perfect for that.

The key to tuning your forehand is to unlearn your developed habit of compensating for racquet misalignment at impact by applying force with the wrist. You need to learn how to swing the racquet fluidly with a completely relaxed wrist.

A good analogy is when you go to the optometrist for the first time in your life to get glasses for near-sightedness. All of your life, you've been squinting in order to see the world. But when the optometrist is measuring the proper corrective power your eyes, it's important that you stop squinting for the first time in your life and let your eyes relax. Otherwise, you'll still need to squint even after you get your glasses or contacts.

So the same applies to tuning the MgR/I value of your racquet. You can't tell whether your MgR/I value is tuned properly if your wrist is not fully relaxed.

If your MgR/I value is slightly lower than your optimum, when you swing with a completely relaxed wrist, the racquethead will lag behind the hand at the moment of impact, causing you to naturally push your shots wide right (assuming you are righthanded). You need to resist the temptation to compensate by applying force from the wrist. It's kind of like when golfer has a slice swing and is less accurate because he has to always compensate for it.

Conversely, if the MgR/I value is slightly above your optimum, then when you swing with a completely relaxed wrist, the racquethead will get ahead of the hand, and you will tend to pull your shots to the left. The temptation here might be to convert the extra angular velocity into more topspin, but again you need to resist.

When your MgR/I value is perfectly tuned, you can simply fling your arm at the ball with a relaxed wrist, and the racquet will naturally stay perpendicular to your target all of the way through the hitting zone. This means that slight timing errors do not get punished. And you will notice that your targeting accuracy when hitting against the wall improves dramatically.

When my MgR/I value is tuned, I can hit a ball within a 1x1 foot square target almost every time. But if my racquet is slightly off, I can't hit as accurately. Compensating for the mistuned angular velocity might allow me to consistently hit the ball within a 3x3-ft square target, but why settle for that? That difference in accuracy is often the difference between winning a match and losing.

If MgR/I is too low, you can add a little more lead to the top of the handle. If it's too high, you can either remove some lead from that spot or add a dab to the tip. Don't settle for almost! Keep adjusting until you get that "in the zone" feeling.

When you are tuning for the first time, you might find it helpful to keep going beyond where it feels good until it's obvious that you've gone too far. You need to learn the difference in feel between MgR/I too low and too high.

Following all of these steps takes a lot of care and patience, but the end result is worth it.

Can you do me a huge favor and tell me what the rating would come to for a Stock strung Donnay 99 gold would be? Also what would I have to add to the racket to get it to 21.0, id like to test the feel of it.

Id do it myself i see the math is pretty simple i just dont know how to find the balance number in cm....

The MgR/I value gives a measure of the racquet's natural swing frequency as it pivots about the wrist axis on a forehand.

A groundstroke can be simply modeled as a double pendulum, with the upper pendulum swinging from the shoulder, and the lower pendulum swinging from the wrist. The speed of the upper pendulum is mostly related to the length of the player's arm, while the speed of the lower pendulum is largely a function of the racquet's weight's distribution. The frequency of a pendulum is proportional to sqrt(MgR/I), where M is the mass of the pendulum, g is the acceleration of gravity, R is the distance from the pivot point to the center of mass, and I is the moment of inertia about the pivot point. Thus, a racquet's MgR/I value gives a measure of it's natural swing frequency. It is not necessary to take the square root, because only relative values are needed.

Click to expand...

Trav, there is something about yopur MgR/I formula I've been wondering about for some time now. What pendulum action around the wrist are you referring to? When you look at slomo movies of e.g. the Federer forehand, you can clearly see that most of the accelleration towards the ball occurs in the horizontal plane (for an example, see http://www.youtube.com/watch?v=xNPaZj4yn00&feature=related). So how does g, the accelleration due to gravity, which only occurs in the vertical plane, affect the pendulum around the wrist? Wouldn't the horizontal accelleration component of the racket arm, as generated by the player, be more important here?

Also, when you look at the pendulum action of the wrist, the wrist remains usually completely laid back up untill the point of contact with the ball. That is, the pendulum action around the wrist joint typically occurs after the ball is hit, during follow-through. Then how can this pendulum motion so crucially affect the stroke and, indeed, a player's ranking if it takes place after ball contact?

The swingweight about the wrist pivot will be different depending on where the player grips the handle. If one chokes down to the bottom of the grip, the swingweight and MgR/I will be higher; if one chokes up, these values will be lower.

Federer and Nadal, for example, hold their racquets at the bottom of the handle (little finger just barely on the grip) on groundstrokes, making their MgR/I numbers lower than they would appear.

I think it would be helpful to establish a reference handle position for comparing MgR/I numbers, i.e. little finger just above the taper of the buttcap.

It would also be helpful to have a conversion for other grip positions - up or down the handle.

Trav, there is something about yopur MgR/I formula I've been wondering about for some time now. What pendulum action around the wrist are you referring to? When you look at slomo movies of e.g. the Federer forehand, you can clearly see that most of the accelleration towards the ball occurs in the horizontal plane (for an example, see http://www.youtube.com/watch?v=xNPaZj4yn00&feature=related). So how does g, the accelleration due to gravity, which only occurs in the vertical plane, affect the pendulum around the wrist? Wouldn't the horizontal accelleration component of the racket arm, as generated by the player, be more important here?

Also, when you look at the pendulum action of the wrist, the wrist remains usually completely laid back up untill the point of contact with the ball. That is, the pendulum action around the wrist joint typically occurs after the ball is hit, during follow-through. Then how can this pendulum motion so crucially affect the stroke and, indeed, a player's ranking if it takes place after ball contact?

I'm looking forward to your explantion.

Thanks,
kaiser

Click to expand...

Good questions, although he did state that its the natural pendulum action, hence why g is used.

My question is: The sample for the data seems pretty small. Only data from 2005 onward was used (Or was it just for 2005?). Since then the top five players has pretty much consisted of the same small group of people. So there is a big chance that the dip in the graph for the top five is simple coincidence.

Good questions, although he did state that its the natural pendulum action, hence why g is used.

My question is: The sample for the data seems pretty small. Only data from 2005 onward was used (Or was it just for 2005?). Since then the top five players has pretty much consisted of the same small group of people. So there is a big chance that the dip in the graph for the top five is simple coincidence.

Click to expand...

I agree that the sample size in this thread is indeed small, but If you look at my MR^2 data thread, where the sample size is large enough to be more statistically robust, there are 8 players within the statistically significant apparent optimal zone of MR^2 = 380-390.

I'll soon post another plot on that thread for MR values, showing that there is a statistically significant apparent optimum zone for MR > 11.75, and that MR > 12.0 appears to be even better.

Only four of the 8 players with 'optimum' MR^2 values have MR values over 11.75: Agassi, Robredo, Gaudio, and Grosjean. All of these 4 were top-5 players under 6' tall with unimpressive serves, ho-hum speed, but exceptionally accurate and reliable groundstrokes that made them top-5 players, so I don't think it is coincidence. Of these 4, only 1 of them has MR value over 12.0: Gaudio. Could it be coincidence that he is the only player on the list from Federer's generation to win a Grand Slam title?

Also, all 6 top-20 players in 'optimum' MR^2 zone are under 6 feet with strength as described for the 4 players mentioned above. Coincidence? One of the other 2 players is Ferrer, a top-5 player who led the tour in % return games won (during the Federer-Nadal era) multiple years! Coincidence?

Good questions, although he did state that its the natural pendulum action, hence why g is used.

Click to expand...

Ok, so why is the natural pendulum action, which is driven by gravity and therefore only in the vertical plane, relevant for the pendulum around the wrist which is mostly in the horizontal plane (in the forehand of the pros) and hence largely immune to gravity? This is something I'd like to understand, so what's up Trav?

Ok, so why is the natural pendulum action, which is driven by gravity and therefore only in the vertical plane, relevant for the pendulum around the wrist which is mostly in the horizontal plane (in the forehand of the pros) and hence largely immune to gravity? This is something I'd like to understand, so what's up Trav?

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Almost every single pro tennis player brings the racquethead above his head on the backswing. As gravity drops the racquethead from that point, the wrist is free to pivot. How fast the racquethead travels as the racquet travels through a high-to-low-to-high pendulum sweep is largely dependent on the relative weight distributions of the arm and racquet.

Trav, there is something about yopur MgR/I formula I've been wondering about for some time now. What pendulum action around the wrist are you referring to? When you look at slomo movies of e.g. the Federer forehand, you can clearly see that most of the accelleration towards the ball occurs in the horizontal plane (for an example, see http://www.youtube.com/watch?v=xNPaZj4yn00&feature=related). So how does g, the accelleration due to gravity, which only occurs in the vertical plane, affect the pendulum around the wrist? Wouldn't the horizontal accelleration component of the racket arm, as generated by the player, be more important here?

Also, when you look at the pendulum action of the wrist, the wrist remains usually completely laid back up untill the point of contact with the ball. That is, the pendulum action around the wrist joint typically occurs after the ball is hit, during follow-through. Then how can this pendulum motion so crucially affect the stroke and, indeed, a player's ranking if it takes place after ball contact?

Julian,
I'm glad to know that....for a moment I thought this post was not about tennis rather math and physics.
do you think pro level players know what these guys are talking about?

Click to expand...

1.Tennis pros do talk to tennis manufacturers.
Some tennis manufacturers know what we are talking about here
2.Some pros are very reluctant to change a racket-
You may talk about Federer and Djokovic and Wozniacki
as representing 3 different cases

Almost every single pro tennis player brings the racquethead above his head on the backswing. As gravity drops the racquethead from that point, the wrist is free to pivot. How fast the racquethead travels as the racquet travels through a high-to-low-to-high pendulum sweep is largely dependent on the relative weight distributions of the arm and racquet.

So the pendulum action you are referring to is a rotation of the wrist around the axis going through the forarm, and not around the axis perpendicular to that going through the wrist (i.e. from thumb to little finger)?

Because if the latter, the pendulum action would be in the plane of the swing path which is mostly in the horizontal plane, and more so when the player meets the ball higher in the bounce. This means gravity, and hence g, would only play a small role in the pendulum action and g would need to be replaced by a, the accelleration of the racket arm executed by the player.

If the pendulum action you're referring to is a rotation around the forearm axis, as in the modern 'windscreen-wiper' stroke, it would be perpendicular to the plane of the swing path and therefore mostly in the vertical plane. Then gravity does play a role, but not exclusively. When you rotate your forearm to bring the rackethead up during the take-back, you store energy in the forearm by twisting the radius and ulna bones relative to each other. When you then bring arm foreward during the stroke, the radius and ulna are forced back into their original position, releasing this stored energy into a rotation of the wrist and, hence, the racket. This rotational force therefore also affects the pendulum action around the wrist, as well as gravity, creating an angular accelleration on top of g.

Shouldn't this also be accounted for in your formula? How would this affect your conclusions?

So the pendulum action you are referring to is a rotation of the wrist around the axis going through the forarm, and not around the axis perpendicular to that going through the wrist (i.e. from thumb to little finger)?

Because if the latter, the pendulum action would be in the plane of the swing path which is mostly in the horizontal plane, and more so when the player meets the ball higher in the bounce. This means gravity, and hence g, would only play a small role in the pendulum action and g would need to be replaced by a, the accelleration of the racket arm executed by the player.

If the pendulum action you're referring to is a rotation around the forearm axis, as in the modern 'windscreen-wiper' stroke, it would be perpendicular to the plane of the swing path and therefore mostly in the vertical plane. Then gravity does play a role, but not exclusively. When you rotate your forearm to bring the rackethead up during the take-back, you store energy in the forearm by twisting the radius and ulna bones relative to each other. When you then bring arm foreward during the stroke, the radius and ulna are forced back into their original position, releasing this stored energy into a rotation of the wrist and, hence, the racket. This rotational force therefore also affects the pendulum action around the wrist, as well as gravity, creating an angular accelleration on top of g.

Shouldn't this also be accounted for in your formula? How would this affect your conclusions?

Click to expand...

1.An observation by OP ( call it a 21 formula) can make sense
2.A justification to the best of my knowledge has a lot of weak points
If one wants to exchange an E-mail on this subject my E-mail address below

So the pendulum action you are referring to is a rotation of the wrist around the axis going through the forarm, and not around the axis perpendicular to that going through the wrist (i.e. from thumb to little finger)?

Because if the latter, the pendulum action would be in the plane of the swing path which is mostly in the horizontal plane, and more so when the player meets the ball higher in the bounce. This means gravity, and hence g, would only play a small role in the pendulum action and g would need to be replaced by a, the accelleration of the racket arm executed by the player.

If the pendulum action you're referring to is a rotation around the forearm axis, as in the modern 'windscreen-wiper' stroke, it would be perpendicular to the plane of the swing path and therefore mostly in the vertical plane. Then gravity does play a role, but not exclusively. When you rotate your forearm to bring the rackethead up during the take-back, you store energy in the forearm by twisting the radius and ulna bones relative to each other. When you then bring arm foreward during the stroke, the radius and ulna are forced back into their original position, releasing this stored energy into a rotation of the wrist and, hence, the racket. This rotational force therefore also affects the pendulum action around the wrist, as well as gravity, creating an angular accelleration on top of g.

Shouldn't this also be accounted for in your formula? How would this affect your conclusions?

Click to expand...

This has nothing to do with windshield wiping.

If you look at the slo-mo vids I posted earlier in this thread of Del Potro and Gonzalez hitting forehands, you can see that the racquethead typically drops from about 7 ft high to about 3 feet high before rising again toward the ball. During the portion of the stroke where the racquethead is dropping those 4 feet, the player does not need to exert much force to accelerate the racquet. Rather, it is gravity plus centripetal acceleration that accelerate the racquet (it matters little that the plane of the swing is not vertical, as long as there is a significant vertical component to the motion). In other words, the motion of the racquet still obeys the physics of a mechanical double pendulum even though the plane of the swing is only partly in the vertical plane.

Only after the racquethead reaches the bottom of the stroke does the player need to apply significant force to keep the racquet moving. This is because the racquet naturally accelerates during the downward part of the stroke (which is mainly gravity powered). But on the upward part of the stroke, the player must apply force to counter the deceleration caused by gravity. I believe that your body naturally senses the inflection point at the bottom of the swing when the motion of the pendulum sweep of your arm switches from acceleration to deceleration, triggering you to begin applying pressure on the handle to keep the racquet moving.

As Corners has mentioned earlier, Rod Cross published an article in 2009 in the American Journal of Physics, showing that the swing of a baseball bat can be modeled as a double pendulum, and that the player must actually apply a reverse-direction couple just before the moment of impact, otherwise the bat pivots too fast from the wrist, causing timing errors. In other words, MgR/I for the baseball bat was too high.

I finally got around to counting strings on string patterns for all the women on Jura's list so that I could convert to strung specs. Then I used 2-segment beam method to approximate swingweights and merged it with Greg Raven's list.

In summary, as I expected, the WTA players cluster at a higher MgR/I value than the men -- shifted up to about 21.1, while the men are at about 20.9.
This was expected because the women are shorter with shorter arms and faster natural swing frequencies.

I haven't posted the chart yet, but I also found that the women with MgR/I within the optimized 20.9-20.3 range and SW > 340 have superior rankings on average. So the women show essentially the same result as the men!

In the OP, Travler only claimed correlation. I'm going to speculate here on possible causations of players with that type setup being better players. Of course, one is a statistical anomaly, which is always possible, but of no value in this conversation.
A direct causation would be players who play with an "optimal" setup will play better - as implied in the title of the thread.
A third possibility is that players with an excellent natural feeling for moving the racket and hitting the ball gravitate toward these racket setups because they feel more efficient and comfortable even if they could play just as well with another setup. At the very top of the tennis game the pros have an ability to sense things unconciously through their innate abilities and repetition. Maybe those with the best sense of tennis in general have the best sense of feeling how the racket moves through the air.

How does this tie in with depolarized vs polarized set ups? I recall reading a thread of yours from several years back that talked about that, curious what your take on it is now (I think it's title was how to set up your racket like an ATP pro).

With the advances in string technology of the last 5 years, plenty of spin can be found with almost any racquet.

So now what separates the contenders from the rest is whether or not the racquet is heavy enough to counter heavy balls and the balance fine-tuned enough to deliver perfect accuracy on every shot. This thread provides evidence to support this. So this thread is my updated version of "How to set up your racquet like an ATP Pro". Actually, it would be more aptly named, "How to set up your racquet like a Top-10 ATP Pro."

With the advances in string technology of the last 5 years, plenty of spin can be found with almost any racquet.

So now what separates the contenders from the rest is whether or not the racquet is heavy enough to counter heavy balls and the balance fine-tuned enough to deliver perfect accuracy on every shot. This thread provides evidence to support this. So this thread is my updated version of "How to set up your racquet like an ATP Pro". Actually, it would be more aptly named, "How to set up your racquet like a Top-10 ATP Pro."

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yup nice work. its just most ppl cant calculate their sw so too bad ^^

Your quote
--->
For maximum control on a groundstroke, the racquet face should remain at a constant angle through the hitting zone. For this to occur, the forward component of the velocity vector of the racquethead must have equal magnitude to the forward component of the velocity vector of the hand. In other words, if the racquethead moves forward faster (or slower) than the hand during the moment of impact, then small errors in timing will result in changes in racquetface angle, leading to less accuracy of the shot. But if the racquethead moves at the same speed as the hand, then small errors in timing are inconsequential and the ball will still go toward the target.
--->
Fig 4 disagrees with your SECOND sentence above

Your quote
--->
For maximum control on a groundstroke, the racquet face should remain at a constant angle through the hitting zone. For this to occur, the forward component of the velocity vector of the racquethead must have equal magnitude to the forward component of the velocity vector of the hand. In other words, if the racquethead moves forward faster (or slower) than the hand during the moment of impact, then small errors in timing will result in changes in racquetface angle, leading to less accuracy of the shot. But if the racquethead moves at the same speed as the hand, then small errors in timing are inconsequential and the ball will still go toward the target.
--->
Fig 4 disagrees with your SECOND sentence above

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The double-pendulum stroke represented in Fig. 4 of the Cross paper is a reasonable simulation for a golf swing or a tennis serve, but not for a forehand.

For a golf swing (or a tennis serve), the ball is stationary (or almost stationary). This means that small errors in timing will not lead to large errors in direction, as they would if the stroke modeled in Fig 4 was used for a forehand.

The stroke of Fig 4 shows that maximum angular velocity of the clubhead is reached right at impact. This is what you want to achieve when hitting a golf ball, because increased angular velocity leads to more power.

On a tennis serve, the same goal applies - maximum racquethead speed is the ideal. So the stroke of Fig 4 is still a good model.

But for a forehand, whipping the racquet toward the ball with maximum angular velocity at impact is not a good way to hit the ball. If you are a fraction of a second late with your timing, the incoming ball will travel further before making contact with the racquet. And when it does, the racquetface will have a much different angle (because it is rotating at maximum angular velocity), causing a big error in shot direction and the ball to spray off to your right (if you are righthanded).

Instead, for a forehand, ideally you want the racquethead to travel at very high speed through the impact zone, but you want the angular velocity (omega2) to be as small as possible. It might be ok for there to be some angular velocity in the vertical plane (for topspin). But when hitting a return of serve, even vertical velocity is best minimized in order to reduce the sensitivity to timing errors.

If you look at slo-mo forehands on tennisone, you can see that the angular velocity of the racquet (around the vertical axis) slows down to zero just before impact, and stay almost zero well after the ball has left the strings.

I would be interested to see if Cross can set the couples C1 and C2 in his model both to zero (or have C1 increase after the bottom of the swing), and then find values for the weights and lengths of the arm and racquet that permit the hand and racquet to move at the same forward speed through the impact zone.

While all this is very interesting and the stats are compelling, did we learn anything really new i.e. different from what intuition and club hacker, honest, experience would have told us?

Lets assume that lower ranked players tried to use rackets with specs of higher ranked players. Would it improved their performance/ranking?

I doubt it. They would not be able to handle succesfully (i.e. winning more matches) the heavier, more demanding sticks.

I am a declining NTRP 4.0 level and while I tried to play with ProStaff 85, PB10 325. Rebel Eox, Diablo Mid etc, I had to admit that the only "shop pro level rackets" I can play with are Prestige Pro and MP YT.

Why? Because they have a very low swingweight.

The top guys would still dominate when using lower ranked guys racket specs, but they just get an extra edge by using more demanding tools.

I used to be a ski instructor and while I can just about ski on female light racers WC skis, I would break my cruciate very quickly if I tried WC level guys planks.

Tennis is less dangerous, but similar rules apply to equipment, I think.

btw the heaviest swinging racket (felt like 340+ swingweight) I ever tried was a demo Volkl PB10 325 stick from UK shop, which is somehow listed as having 320 swingweight on TW website. It was not visibly leaded up (I removed the grip to check) but unplayable in match condition for someone of my level.

How much lead do I need to add to my Prestige Pro to experience swingweight of 370

The double-pendulum stroke represented in Fig. 4 of the Cross paper is a reasonable simulation for a golf swing or a tennis serve, but not for a forehand.

For a golf swing (or a tennis serve), the ball is stationary (or almost stationary). This means that small errors in timing will not lead to large errors in direction, as they would if the stroke modeled in Fig 4 was used for a forehand.

The stroke of Fig 4 shows that maximum angular velocity of the clubhead is reached right at impact. This is what you want to achieve when hitting a golf ball, because increased angular velocity leads to more power.

On a tennis serve, the same goal applies - maximum racquethead speed is the ideal. So the stroke of Fig is a good model.

But for a forehand, whipping the racquet toward the ball with maximum angular velocity is not a good way to hit the ball. If you are a fraction of a second late with your timing, the incoming ball will travel further before making contact with the racquet. And when it does, the racquetface will have a much different angle (because it is rotating at maximum angular velocity), causing a big error in shot direction and the ball to spray off to your right (if you are righthanded).

I would be interested to see if Cross can set the couples C1 and C2 in his model both to zero (or have C1 increase after the bottom of the swing), and then find values for the weights and lengths of the arm and racquet that permit the hand and racquet to move at the same forward speed through the impact zone.

Click to expand...

Hi,

1.His paper can be transferred from his Web site if you do NOT have it

2.He his an appendex with equations for "both pendula"
I have to see what will happen with C1 and C2 both set to zero
I have a paper copy on me.
3.I disagree with your sentence starting with "But for a forehand"-
there are some experimental data disagreeing with you.
See references in the paper,PROBABLY one of them by Brian Gordon.
He maybe discussing a related issue,but I am NOT sure.
I will do some checking and I will correct my post if necessary
Please seehttp://tt.tennis-warehouse.com/showthread.php?t=386651&page=2
post #31
It refers to FOREHAND,I believe.
You may want to check with John Yandell
regards,
Julian

Here is an example that shows how the angular velocity of the racquet is very high as the racquet approaches the ball, but then slows down just before impact. Note how (in slo-mo time scale) that Gonzo's racquet rotates through ~90 degrees in the 2-second duration that it takes from the racquet to enter the field of view to when it impacts the ball (from the racquetface facing the screen, to an orientation perpendicular to the screen). And then during the next two seconds (mostly after impact), the racquet hardly rotates at all (it stays oriented perpendicular to the screen).

You can see the angular velocity by noticing how much the angle of the handle changes relative to your view between frames. I have looked through other players like Federer, Djokovic, and Soderling. And this pattern is the same for all of them.

Actually, the curves for omega2 in Fig2 of cross's paper (where C2 is set to zero) look more like the videos!

So I don't think there is a contradiction between my statements and Cross's simulations.